A scatter plot is a graph that shows how two quantitative variables are related by plotting paired data values as points. The x-axis usually shows the explanatory variable, and the y-axis usually shows the response variable. Scatter plots matter because they help you see patterns that are hard to notice in a table of numbers.
They are used in science, economics, sports, health, and engineering to study relationships between measurements.
To read a scatter plot, look at the direction, form, and strength of the point pattern. Direction tells whether y tends to increase or decrease as x increases, form tells whether the pattern is roughly linear or curved, and strength tells how closely the points follow the pattern. Outliers and clusters are important because they may reveal unusual cases, measurement errors, or hidden groups in the data.
Correlation measures the strength and direction of a linear relationship, but it does not prove that one variable causes the other.
Key Facts
- Each point in a scatter plot represents one ordered pair: (x, y).
- The explanatory variable is usually placed on the x-axis, and the response variable is usually placed on the y-axis.
- A positive association means y tends to increase as x increases.
- A negative association means y tends to decrease as x increases.
- The correlation coefficient r satisfies -1 ≤ r ≤ 1 and describes the direction and strength of a linear relationship.
- A line of best fit can be written as y = mx + b, where m is the slope and b is the y-intercept.
Vocabulary
- Scatter plot
- A graph that displays paired numerical data as points on a coordinate plane.
- Explanatory variable
- The variable plotted on the x-axis that may help explain or predict changes in another variable.
- Response variable
- The variable plotted on the y-axis that is measured as an outcome.
- Correlation
- A measure of the direction and strength of a linear relationship between two quantitative variables.
- Outlier
- A data point that lies far away from the overall pattern of the other points.
Common Mistakes to Avoid
- Putting the variables on the wrong axes is wrong because the explanatory variable usually belongs on the x-axis and the response variable belongs on the y-axis.
- Assuming correlation proves causation is wrong because two variables can be related without one directly causing the other.
- Ignoring outliers is wrong because an unusual point can strongly affect the apparent trend, correlation, and line of best fit.
- Describing only direction and forgetting strength and form is wrong because a complete scatter plot description should include direction, form, strength, and unusual features.
Practice Questions
- 1 A student records study time and test score as (1, 62), (2, 70), (3, 75), (4, 83), and (5, 88). Describe the direction of the association and estimate the change in score for each additional hour studied.
- 2 For a line of best fit y = 4.5x + 32, predict y when x = 6. Then interpret the slope in the context of a scatter plot.
- 3 A scatter plot shows a strong positive association between ice cream sales and number of people at a beach. Explain why this does not prove that ice cream sales cause more people to go to the beach.